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PAUL SCHERRER INSTITUTPAUL SCHERRER INSTITUT
Electrical transport and magnetic interactions in 3d and 5d transition
metal oxides
Laboratory for Developments and Methods, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
Kazimierz Conder
For the past decades, a tremendous amount of effort has been devoted to exploring the nature of 3d transition metal oxides where various exotic states and phenomena have emerged such as:• high-Tc cuprate superconductivity• colossal magnetoresistivity• metal-insulator transitions
Motivation
It has been established that these states and phenomena are caused by strong cooperative interactions of spin, charge, and orbital degrees of freedom.
3
Lattice
Chargeorder
Spinorder
Orbitalorder
Spin, charge, orbital and lattice degrees of freedom in strongly correlated electron systems
Higher cation charges:• smaller radius• smaller coord. numbers
Number of (unpaired) electrons:• spin• charge
Occupied and unoccupied orbitals
Bond anisotropy
Crystal field splittingJahn-Teller effect
Spin-orbit interaction
Electrical properties of transition metal oxides
• The d-levels in most of the transition metal oxides are partially filled.
• According to band structure calculations half of the known binary compounds should be conducting.
Empty or completely filled
d-band (d0 or d10)
Partly filled
d-band
http://wps.prenhall.com/wps/media/objects/3085/3159106/blb2406.html
Energies of the d orbitals in an octahedral crystal field.
Completely filled
orbitals: d6
Orbital interaction with the lattice
Orbitals are nearby O2-
Orbitals are between O2-
Octahedral crystal field
TiO- rutileTi
O
Ti2+ 3d24s0
metal
NiO- NaCl structure Ni2+ 3d84s0
Is insulator!Why not a metal?
Ni
O
CuO Cu2+ 3d94s0
CoO Co2+ 3d74s0
MnO Mn2+ 3d54s0
Cr2O3 Cr3+ 3d34s0
Odd number of d electrons-all this oxides should be metals but are insulators
Whatever is the crystal field splitting the orbitals are not fully occupied!!!
Why not metal?
3d74s23d54s2 3d94s23d44s2 Electron configurations of elements
8
Mott-Hubbard insulators(on site repulsive electron force)
Sir Nevill
Francis Mot Nobel Prize in Physics 1977
•Most of the oxides show insulating behavior, implying that the d-electrons are localized.•Short-range Coulomb repulsion of electrons can prevent formation of band states, stabilizing localized electron states.
W
W
U
Density of states
Upper Hubbard band
Lower Hubbard band
FL
Density of states
W FL
U
U<W U>W
Ni2+ + Ni2+ → Ni3+ + Ni+ d8 + d8 → d7 + d9
Correlation energy, Hubbard
U
Band width=W
small
large Electron transferCoulomb repulsiveforce
e-
9
Mott-Hubbard insulator Charge Transfer insulator
10
Electrons have not only charge but also spin!
11
Magnetic order in transition metal oxides
Diamagnetism
Paramagnetism
Ferromagnetism
Antiferromagnetism
Ferrimagnetism
Magnetit (Fe3O4) inverse spinel.
Ferrimagnet.
Fe2+ 3d6 Fe3+ 3d5
Octahedral coordination
Tetrahedral coordination
Superexchange
Superexchange is a strong (usually) antiferromagnetic coupling between two nearest neighbor cations through a non-magnetic anion. • because of the Pauli Exclusion
Principle both spins on d and p hybridized orbitals have to be oriented antiparallel.
• this results in antiparallel coupling with the neighbouring metal cation as electrons on p-orbital of oxygen are also antiparallel oriented.
Pauli Exclusion Principle
Goodenough–Kanamori–Anderson Rules
dz2
dx2
−y2
dz2
180o – Exchange between half occupied or empty orbitals is strong and
antiferromagnetic
Ferromagnetic superexchange - ferromagnetic when angle 90o
0.0 0.1 0.2 0.310
100
La2-x
SrxCuO
4
Insu
lato
r
Met
al
An
tife
rro
ma
gn
et
Superconductor
TN
TC
Tem
pera
ture
[K]
Sr-content x, (holes per CuO2-layer)
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La, Sr
Cu
O
(LaBa)2CuO4 TC=35K K.A. Müller und G. Bednorz (IBM Rüschlikon 1986, Nobel price 1987)
High Temperature Superconductor: La2-
xSrxCuO4
Undoped superconducting cuprates are antiferromagnetic Mott insulators!
Double-exchange mechanism
Magnetic exchange that may arise between ions on different oxidation states!
• Electron from oxygen orbital jumps to Mn 4+ cation, its vacant orbital can then be filled by an electron from Mn 3+.
• Electron has moved between the neighboring metal ions, retaining its spin.
• The electron movement from one cation to another is “easier” when spin direction has not to be changed (Hund's rules).
Mn 3+ d4 Mn 4+ d3
O2- 2p
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FerromagneticMetal
ParamagneticInsulator
La1-xCaxMnO3. Double exchange mechanism. The electron movement
from one cation to another is “easier” when spin direction has not to be changedNote that no oxygen sites are shown!
17A.P. Ramirez, J. Phys.: Condens. Matter., 9 (1997) 8171
CMR (colossal magnetoresistance) La0.75Ca0.25MnO3
Tc
)(
)()0(
HR
HRHRR
Magnetoresistance is defined as the relative change of resistances at different magnetic field
Tc
FerromagneticMetal
ParamagneticInsulator
✓ 4d and 5d orbitals are more extended than 3d’s✓ reduced on-site Coulomb interaction strength✓ sensitive to lattice distortion, magnetic order, etc.✓ spin-orbit (SO) coupling much stronger
5d vs. 3d transition metal oxides
PRB, 74 (2006) 113104
• 4d and 5d orbitals are more extended than 3d’s
• Reduced Coulomb interaction
Heungsik Kim et al., Frontiers in Condensed Matter Physics, KIAS, Seoul, 2009
Insulator
Metal
Insulator
Sr2IrO4Under the octahedral symmetry the 5d states are split into t5
2g and eg orbital states. The system would become a metal with partially filled wide t2g band.
PRL 101, 076402 (2008)
Jeff = |S – L| is an effective total angular momentum defined in the t2g manifold with the spin S and the orbital angular L momenta.
An unrealistically large U>> W could lead to a Mott insulator. However, a reasonable U cannot lead to an insulating state as already 4d Sr2RhO4 is a normal metal. By a strong Spin-Orbit
(SO) coupling the t2g band splits into effective total angular momentum Jeff=1/2 doublet and Jeff=3/2 quartet bands.
The Jeff=1/2 spin-orbit states form a narrow band so that even small U opens a Mott gap, making it a Mott insulator
The formation of the Jeff bands due to the large SO coupling energy explains why Sr2IrO4 is insulating while Sr2RhO4 is metallic.
Opposite directions of electronic orbital motions around a nucleus occur with the same probability, and thereby cancel each other.
Interaction between the electron's spin and the magnetic field generated by the electron's orbit around the nucleus.
Spin and orbital motion have the same directions. The spin-orbit correlation suppresses the transfer of electrons to neighboring atoms making Sr2IrO4 an insulator.
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Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
Crystal structure of Na2IrO3
monoclinic space group C 2/m
PRB 88, 035107 (2013)
Iridium honeycomb layers stacked along the monoclinic c axis
For both Na2IrO3 and Li2IrO3 a honeycomb structure is observed enabling a realization of the exactly solvable spin model with spin liquid ground state proposed by Kitaev.
23
J1=0 J2=0J1=2J2
Heisenberg exchangeKitaev exchange
A Spin Liquid (Figure Credits: Francis Pratt, STFC)
Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
J>0 ferromagnetic
J<0 antiferromagnetic
PRL 105, 027204 (2010)
24
Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
A Spin Liquid (Figure Credits: Francis Pratt, STFC)
• Na2IrO3 and Li2IrO3 order magnetically at 15K
• I was suggested (PRB 84, 100406
(2011)) that the reduction of the chemical pressure along the c-axis can induce spin glass behavior.
• This can be achieved either by exerting pressure in the ab plane or substituting Na by smaller Li ions.
• Antiferromagnetic transition around 15K for the parent compound Na2IrO3.
• This is suppressed for the doped sample.
K. Rolfs, S. Toth, E. Pomjakushina, D. Sheptyakov, K. Conder, to be published
Na2-xLixIrO3 with x = 0, 0.05, 0.1 and 0.15
Magnetization measurements of Na1.9Li0.1IrO3 in 0.1T. Real and imaginary part of the AC susceptibility measured at different frequencies.
The cusp is frequency dependent which is characteristic for the spin-glass phase
Na1.95Li0.05IrO3
Na2IrO3
Gla
ssy
state
For higher doping spin-glass state
26
Conclusions Electrical transport properties in transition metals (Mott insulators):• crystal field splitting• Coulomb repulsion
Colossal magnetoresistivity:• crystal field splitting• orbital order
5d iridates:• crystal field splitting• spin-orbit interaction
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